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ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 1
Fatigue of metals, view point and prospect
a b c andré bignonnet consulting
Fatigue & structural durability
andre.bignonnet@wanadoo.fr
Action Nationale de Formation (ANF)
METALLURGIE FONDAMENTALE
22 -25 Octobre 2012 à Aussois
Mechanical engineering applications
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 2
-1.1
-0.1
0.9
0 360
Sa
Sm
What will be the response of a structure under a cyclic loading?
.....
Mechanical engineering applications
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 3
Structures under cyclic loading Asymptotic states Asymptotic behavior of elasto-visco-plastic structures under thermomechanical cyclic loading: Elasticity Elastic shakedown stabilized response Plastic shakedown ratcheting
Mechanical engineering applications
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 4
104 106 108 cycles
Str
ess a
mp
litu
de
0.1
1
10
1.E+02 1.E+03 1.E+04 1.E+05
% Delta e élastique
% Delta e plastique
% Delta e totale
Pla
sti
c s
tra
in
am
pli
tud
e
102 103 104 cycles
High Cycle Fatigue (HCF) Low Cycle Fatigue (LCF)
Fatigue life Elasticity & elastic shakedown
Fatigue life Inelasticity , plastic shakedown
+ mean stress effect
Multiaxial stress & strain effect Small size defects & nonmetallic inclusions
Mechanical engineering applications
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 5
104 106 108 cycles
Str
ess a
mp
litu
de
0.1
1
10
1.E+02 1.E+03 1.E+04 1.E+05
% Delta e élastique
% Delta e plastique
% Delta e totale
Pla
sti
c s
tra
in a
mp
litu
de
102 103 104 cycles
High Cycle Fatigue (HCF) Low Cycle Fatigue (LCF)
Objective life Objective life
Ad
mis
sib
le f
ati
gu
e l
oa
din
g
Ad
mis
sib
le f
ati
gu
e l
oa
din
g
Define a technical specification
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 6
Outline
shakedown theory / fatigue concept
high cycle fatigue and low cycle fatigue
Mechanical engineering applications
View point & prospect
The shakedown theory / fatigue concept
Daniel C. Drücker, 1963
’When applied to the microstructure, there is a hope that the concepts of endurance limit and shakedown are related
and that fatigue failure can be related to energy dissipated in idealized material when shakedown does not occur ’’
On the macroscopic theory of inelastic stress-strain-time-temperature behavior.
in AGARD – Advances in material researchs in the NATO Nations pp 193-221, January 1963
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 7
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 8
The shakedown theory / fatigue concept
A POSSIBLE APPROACH:
THE MATERIAL IS CONSIDERED AS A STRUCTURE (MICRO-
STRUCTURE) SUBMITTED TO CYCLIC (VARIABLE) LOADINGS
Mathematical Results (Melan, Koiter theorem…)
Results on the Theory of polycristalline agregates
t
- t
B
r
A
Meso macro relationship
E. Orowan, 1939,
A theory of the fatigue of metals, Proc. Royal Soc., London, A, pp171-179
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 9
The shakedown theory / fatigue concept
Meso/Macro Scales, Cyclic behaviour, Shakedown
LCF
MACRO Structure
MESO Grain
Ratcheting elastic shakedown plastic shakedown
Energy dissipation!
HCF
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 10
The shakedown theory / fatigue concept
High Cycle Fatigue criterion
first damage grains : Meso scale Scale of material description for relevant parameters ?
Meso scale Macro scale
LIN-TAYLOR: E==e+p
=l.L-1. +l.(p- Ep)
If p p, 0,
(SACHS), wp Wp residual stress from loading cycle,
strongly dependant of the loading path
EpE,,p ,,
:A (K:)
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 11
The shakedown theory / fatigue concept
At shakedown (x,t) = (x,t) + (x)
Polycyclic Fatigue criterion: f((x,t) )< 0 no fatigue
f((x,t) ) a t(t)+p(t)
t: shear; p=(Trace )/3
ij
rs
-
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 12
MACRO Elastic (or Shakedown)
MESO reasoning on a slip plane
Schmidt Law
tY
N Plastic shakedown elastic
Dang Van Criteria: Papadopoulos, ...
Shakedown parameter
btaptt
)()(max t
t
bounded dissipated energy
HCF : shakedown & dissipated energy
The fatigue limit correspond to the limit of the
elastic shakedown possibility of the material in the structure
at the macro scopic scale and the meso scopic scale
Difficult to estimate:alternative approach in meso stress
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 13
MACRO
Charkaluk & Constantinescu [2001] Maitournam [2001]
• fatigue life determined by stabilized cycle at saturation point
load
N f
lifetime
N N sat
N f = N = f(Wsat)
MESO Skelton [1991]
• constant cumulated dissipated
energy at saturation point
LCF Criterion W= C.N b
LCF : shakedown & dissipated energy
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 14
Research, on each shear plane, of the smallest circumscribed circle
of the loading path
HCF : Mechanical engineering applications
n r
DANG VAN’S CRITERION
The fatigue criterion is : t + a .p < B
t (t)
t * Shear plane
Computation of t (t) et p(t) at each instant
t : shear amplitude on the critical plane
p : hydrostatic pressure
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 15
HCF : Mechanical engineering applications
Hydrostatique pressure 0
B
BpC C
D
-at
Stress path
in the structure
Material data shear amplitude
a security area
damage area
tc
A
B
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 16
HCF : Mechanical engineering applications
t
p
Mooring chains,
deep offshore oil and gas
Operation loading
Complex cyclic loading
introduced in the calculation
Tension variation
In plane bending
Out of plane bending
results
in the Dang Van diagram
2
3
x
x x 1
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 17
HCF : Mechanical engineering applications
- 600
- 500
- 400
- 300
- 200
- 100
0
100
200
0 1 2 3 4 Profondeur (mm)
Contr
ain
tes ré
sid
uelles ( M
Pa )
RR qq ZZ
- 600
- 500
- 400
- 300
- 200
- 100
0
100
200
0 2 3 4 Profondeur (mm)
Contr
ain
tes ré
sid
uelles ( M
Pa )
RR qq ZZ
FATIGUE CALCULATION OF A ROLLED CRANKSHAFT
- 0.42
- 0.48
- 0.54
- 0.60
- 0.65
- 0.71
- 0.77
- 0.78
- 0.88
- 0.94
- 1.00
- 0.42
- 0.48
- 0.54
- 0.60
- 0.65
- 0.71
- 0.77
- 0.78
- 0.88
- 0.94
- 1.00
ISO VALUES
OF DANG VAN’S
CRITERION
RESIDUAL
STRESSES
FROM ROLLING
APPLIED
LOAD
LOAD PATH
AT CRITICAL
POINT
M/RR M/ qq
M/ZZ
- 600
- 400
- 200
0
200
400
600
800
1000
0 200 400 600 800
Angular position (°)
M/RR M/ qq
M/ZZ
M/RR M/ qq
M/ZZ
- 600
- 400
- 200
0
200
400
600
800
1000
0 200 400 600 800
0
50
100
150
200
250
300
350
400
- 400 - 300 - 200 - 100 100 200
Pression hydrostatique ( MPa S
hear
(Mpa)
0 0
50
100
150
200
250
300
350
400
- 400 - 300 - 200 - 100 100 200
Hydrostatic pressure (Mpa)
0
Design curve
Rolled Not rolled
Mom
ents
(N
.m)
HCF : Mechanical engineering applications
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 18
0.6 a
0
t, shear
amplitude
ta max
p
p residual
Crack initiation only possible due to extremely severe braking which induced residual hoop stress > +400 MPa
Fatigue failure analysis of railroad vehicles wheel
Contact fatigue
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 19
LCF : Mechanical engineering applications
• cyclic softening / hardening
• stabilised behaviour
• final failure
Load
number of cycles
stabilisation
Nf Nsta
N Skelton (1991)
40°C
750°C
*
*
w
Stabilised cycle :
representative of the cyclic life
of the structure
Failure of the structure :
initiation of a macroscopic
crack
Charkaluk and Constantinescu (2000)
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 20
LCF : Mechanical engineering applications
Material and structural behaviour model in structural calculation
Representation of the material in the structure by constitutive equations with parameters of easy access
coupling with damage : leads to difficulties in
parameter identification
numerical implementation
calculation time
without coupling with damage
evolution cycle by cycle of the structure is sometime not necessary
identification on steady-state cycles and structural aged representativity
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 21
LCF : Mechanical engineering applicatio
Exhaust pipe
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 22
LCF : Mechanical engineering applications
10
100
1000
10000
10 100 1000 10000experimental lifetime
es
tim
ate
d l
ife
tim
e
Isothermal LCF
TMF on specimens
TMF on exhaust-manifolds
w
N
W= C.N b
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 23
conclusion
High Cycle Fatigue: the structure is globaly elastic and fatigue phenomenon only
initiates in some grains.
The fatigue limit corresponds to
the shakedown limit at the meso scale
One can evaluate the local stress at the stabilized state :
from (x,t), we derive the local stress by constructing the
smallest hypersphere that contains (x,t) and gives an
estimation of the local stress tensor (t)=(t)+ From meso-macro relationship:
The fatigue criterion is given by:
t(t) + ap(t) ≦ B
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect 24
conclusion
Low Cycle Fatigue: The macroscopic plastic strain is important and difference
between p and p decreases so that there is few differences
between MACRO and MESO parameters.
The dissipated energy per cycle at the stabilised state is proposed as a fatigue criterion
W= C N b
it is a scalar parameter easy to compute
which leads sometimes to fairly good predictions on structures
PROSPECT…..
Dissipation, temperature & Shakedown limit
Luong(1995)
Flexion rotative
Acier XC55
Thermographie IR (moyenne)
Strohmeyer(1914)
Torsion alternée
Acier doux Bessemer
Calorimétrie
Berthel(2007)
Traction alternée
Acier Dual-Phase
Thermographie IR (champ macro.)
Dissipative phenomena & cyclic plasticity : temperature
Stabilized temperature evolutions : asymptotic regime
Shakedown limit characterisation? Which scale? Microstructure influence?
ANF Métallurgie fondamentale 2012 25 Fatigue of metals view point & prospect
Does crack initiation correspond to a source of stored energy? Why nano materials get high strength?
Dissipation, temperature : micro scale
Coupled measure of strain fields & temperature
Steel 316L overquenched polycrystalin (grains mm)
Plasticity activation : critical resolved shear stress, stored energy
Coupling test / numerical simulations : cristal thermoplasticity
Taux de stockage
intragranulaire d’énergie
Microstructure après
essai
Systèmes de glissement
activés
Front de température durant
la sollicitation
Monotonic loading Bodelot (2008), Seghir (2011)
ANF Métallurgie fondamentale 2012 26 Fatigue of metals view point & prospect
Objective : microstructural effect on asymptotic regimes under cyclic loading?
27
100 µm
Tomographie
X HR :
Inclusions
MnS σD(θ°)
/σ
D(0
°)
0,6
0,7
0,8
0,9
1
1,1
0 45 90
Test Direction
σ(θ
°) / σ
(0°)
100
1000
1 10 100 1000
d
Mean defect size
C35
Metasco
MC
42CD4
2. Procédés de fabrication et tenue en fatigue (E. Pessard)
Process & metallurgical parameters: micro scale
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect
Probabilist multiaxial Criterion including two damage mechanisms depending on the type of the leading microstructural heterogeneities.
28
3. Simulation agrégat polycristallin (C. Robert)
Polycristalline agregates modeling: micro scale
ANF Métallurgie fondamentale 2012 Fatigue of metals view point & prospect
With a sufficiently large number of different microstructures investigated, a critical analysis of the multiaxial fatigue criteria has been undertaken, using the local mechanical quantities.